International Journal of Modern Physics E

In this paper, we show two matrices that have identical eigenvalues but different eigenfunctions. This shows that in obtaining two-body nuclear matrix elements empirically, it is not sufficient to consider only energy levels. Other quantities like transitions must also be included.

A systematic study of the super-deformed (SD) bands in $A\sim 150$ mass region is carried out by using two different approaches, namely, the Principal-axis Cranking (PAC) and the Variable Moment of Inertia (VMI). Both these approaches not only support each other’s results but also their hand-in-hand calculations help us in establishing the prominent features, like the band-head spin, parity, quadrupole moment and excitation energy, of the observed SD bands. Since the rotational frequency in the PAC model depends on angular momentum, parity, and quadrupole moment, by identifying the most common rotational frequency between the calculations and the experimentally observed ones, the band-head spin, and parity are likely to be extracted. On the other hand, the VMI model calculations are quite simple and are capable of predicting the threshold limits of band-head spin, the quadrupole moment, and the excitation energy, which in turn are significantly useful for deciding an appropriate configuration assignment in the PAC model calculations of the existing as well as upcoming SD bands. Further, the VMI model calculations involve the variation of the moment of inertia with angular momentum, which in turn is quite helpful in understanding the mechanism of the observed identical SD bands between a pair of neighboring nuclei.

The isotope ${}^{16}\mathrm{\text{O}}$ is one of the most abundant light isotopes, and therefore the process ${}^{16}\mathrm{\text{O}}{(n,\gamma )}^{17}\mathrm{\text{O}}$ reaction plays a critical role in stellar nucleosynthesis. Reaction cross-sections and rates for neutron capture by ${}^{16}\mathrm{\text{O}}$ at astrophysical energies have been calculated with special attention to low-lying, narrow resonances while implementing $R$-matrix formalism during integration.

The two-dimensional intermittency and its self-affine nature are investigated for p–p collisions at $\sqrt{s}=13$TeV in the two-dimensional anisotropic $(\eta -\varphi )$ space. The UrQMD model has been employed to generate and accumulate the p–p collisions data. Our investigation is made in the framework of scaled factorial moment (SFM) method. The concept of Hurst exponent $H$ is incorporated to bring a qualitative comparison between the UrQMD generated minimum bias (MB) events and the events at a particular impact parameter $b=0.4$ fm. The variation of the fractal strength with the variation of $H$ as well as with the variation of the order of the moment $q$ has been analyzed. Also, the nonlinearity in the variation of SFM with that of $H$ has been accompanied in this paper. It is observed that the fractal strength and the intermittent type of fluctuations are found to be much stronger in the region with $H<1$ compared to the region with $H>1$ and the self-affine nature in the fluctuations increases as $H$ deviates from unity.

This paper studies the quark condensate, magnetic moment, magnetic polarization, and magnetic susceptibility in a strong external magnetic field by employing the Dyson–Schwinger equations (DSE). The results show these physical quantities as functions of the magnetic field. We note that the quark’s spin polarizations are approximately proportional to the magnetic field magnitude. For comparison, we investigate the magnetic moments and susceptibility of the nucleon in the constituent quark model framework and demonstrate that both these quantities increase as the magnetic field rises.

The method of description of the high-spin states, which was previously developed and applied for the states of this type in ${}^{208}$Pb, is generalized for the case of the states having more complex multiphonon structure. In this method, the harmonic approximation with the renormalized phonons is used in which the phonons themselves are determined within the nonlinear version of the model based on the random-phase approximation (RPA) and including both the RPA correlations and the beyond-RPA ones. The mean field and the residual interaction are derived within the framework of the self-consistent RPA from the energy-density functional of the Skyrme type. The method is applied for the analysis of the available experimental data in doubly magic ${}^{208}$Pb and ${}^{40}$Ca and in semi-magic ${}^{90}$Zr.